A fractional differential equation with multi-point strip boundary condition involving the Caputo fractional derivative and its Hyers–Ulam stability

Abstract

In this work, we investigate the existence, uniqueness, and stability of fractional differential equation with multi-point integral boundary conditions involving the Caputo fractional derivative. By utilizing the Laplace transform technique, the existence of solution is accomplished. By applying the Bielecki-norm and the classical fixed point theorem, the Ulam stability results of the studied system are presented. An illustrative example is provided at the last part to validate all our obtained theoretical results.

Analysis of implicit system of fractional order via generalized boundary conditions

“…Recently, researchers continuously focus on studying the solution of s in the sense of four main types of stability, that is, Ulam-Hyers stability ( ), generalized Ulam-Hyers stability ( ), Ulam-Hyers-Rassias stability ( ), and generalized Ulam-Hyers-Rassias stability ( ). Ulam's type stability was initially introduced by Ulam [18] in 1940 and has since been investigated and generalized by a number of mathematicians using various approaches [19][20][21][22][23][24].…”

Robust uniform stability criteria for fractional‐order gene regulatory networks with leakage delays

“…Compared with the conventional integer-order model, fractional-order systems have infinite memory and more degrees of freedom. [16][17][18][19][20][21] Because of these advantages, the integration of fractional-order calculus into the nonlinear dynamical system has gained attention and resulted in several new developments in this domain. [22][23][24][25][26][27] To mention a few, Ali et al analyze the existence and delay-dependent uniform stability issues of BAM type fuzzy Hopfield neural networks with both leakage and time delays with the help of Cauchy Schwartz inequality.…”

“…Fractional calculus has gained greater attention in recent years, due to its increasing applications in several fields, such as biology, biophysics, chemistry, and signal processing. Compared with the conventional integer‐order model, fractional‐order systems have infinite memory and more degrees of freedom 16–21 . Because of these advantages, the integration of fractional‐order calculus into the nonlinear dynamical system has gained attention and resulted in several new developments in this domain 22–27 .…”

Application of some special operators on the analysis of a new generalized fractional Navier problem in the context of q-calculus

“…In broad fields such as chemistry, biology, physics, economics, engineering, and so on fractional calculus, related differential equations and BVPs are commonly used [1][2][3][4][5]. In a vast domain of papers, scientists have examined numerous mathematical procedures across different facets of fractional differential equations [6][7][8][9][10][11][12][13].…”